For solution of weak electrolytic, the degree of ionization

Options

A. Will be reciprocal to the dilution
B. Will be proportional to dilution
C. Will be proportional to the square root of dilution
D. Will be proportional to concentration of electrolyte

Answer

To solve the question regarding the relationship between the degree of ionization (α) of a weak electrolyte and its dilution, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Degree of Ionization**: The degree of ionization (α) is defined as the fraction of the total number of molecules of the electrolyte that dissociate into ions when dissolved in a solvent.

2. **Ostwald's Dilution Law**: According to Ostwald's dilution law, for a weak electrolyte, the degree of ionization can be expressed in terms of its ionization constant (K) and its concentration (C). The formula is given as:
\[ \alpha^2 = \frac{K(1 - \alpha)}{C} \]

3. **Assumption for Weak Electrolytes**: For weak electrolytes, the degree of ionization (α) is very small. Therefore, we can assume that \(1 - \alpha \approx 1\). This simplifies our equation to:
\[ \alpha^2 \approx \frac{K}{C} \]

4. **Rearranging the Equation**: From the simplified equation, we can express α as:
\[ \alpha \approx \sqrt{\frac{K}{C}} \]

5. **Understanding the Relationship**: The concentration (C) is inversely related to the degree of ionization. As the concentration decreases (which corresponds to an increase in dilution), the degree of ionization increases. This indicates that:
\[ \alpha \propto \sqrt{\frac{1}{C}} \quad \text{or} \quad \alpha \propto \sqrt{\text{dilution}} \]

6. **Conclusion**: Therefore, we conclude that for a solution of a weak electrolyte, the degree of ionization is proportional to the square root of the dilution.

### Final Answer:
The degree of ionization (α) for a solution of a weak electrolyte is **proportional to the square root of the dilution**.